Nate Silver 2012, The Signal and the Noise:
# ch5
Earthquakes kill more people than hurricanes, in fact,16 despite seeming like the rarer phenomenon.17 Perhaps that is because they are so seldom predicted successfully. Whereas the landfall position of hurricanes can be forecasted at least three times more accurately now than they were even twenty-five years ago, the science of earthquake forecasting seems barely to have evolved since the ninth century A.D., when the Japanese first claimed to be able to anticipate earthquakes by looking at the behavior of catfish.18 (Cows, pigs, eels, rats, parakeets, seagulls, turtles, goldfish, and snakes have also been reported at various times to behave unusually in advance of an earthquake.)
We all know that California is very seismically active; the USGS estimates that an earthquake of magnitude 6.8 or higher will hit San Francisco about once every thirty-five years. Many of you will also know that Alaska has many earthquakes-the second largest one in recorded history, magnitude 9.4, hit Anchorage in 1964.
But did you know about Charleston, South Carolina? It is seismically active too; indeed, it experienced a magnitude 7.3 earthquake in 1886. The USGS estimates that there will be another big earthquake there about once per six hundred years. If you live in Seattle, you should probably have an earthquake plan ready; it is more earthquake-prone than many parts of California, the USGS says. But you don't need one if you live in Denver, which is a safe distance away from any continental boundaries.
If you compare the frequencies of earthquakes with their magnitudes, you'll find that the number drops off exponentially as the magnitude increases. While there are very few catastrophic earthquakes, there are literally millions of smaller ones-about 1.3 million earthquakes measuring between magnitude 2.0 and magnitude 2.9 around the world every year.27 Most of these earthquakes go undetected-certainly by human beings and often by seismometers.28 However, almost all earthquakes of magnitude 4.5 or greater are recorded today, however remote their location. Figure 5-3a shows the exponential decline in their frequencies, based on actual records of earthquakes from January 196429 through March 2012.30
According to the power law that Gutenberg and Richter uncovered, that means that an earthquake measuring between 6.0 and 6.9 should occur about once every thirty years in Tehran.
Furthermore, it follows that an earthquake that measured 7.0 or greater would occur about once every three hundred years near Tehran. This is the earthquake that Susan Hough fears. The Haiti earthquake of 2010, which measured magnitude 7.0 and killed 316,000,32 showed the apocalyptic consequences that earthquakes can produce in the developing world. Iran shares many of Haiti's problems-poverty, lax building codes, political corruption33-but it is much more densely populated. The USGS estimates, on the basis of high death tolls from smaller earthquakes in Iran, that between 15 and 30 percent of Tehran's population could die in the event of a catastrophic tremor there.34 Since there are about thirteen million people in Tehran's metro area, that would mean between two and four million fatalities.
Large earthquakes are almost always followed by dozens or even thousands of aftershocks (the 2011 earthquake in Japan produced at least 1,200 of them). These aftershocks follow a somewhat predictable pattern.35 Aftershocks are more likely to occur immediately after an earthquake than days later, and more likely to occur days later than weeks after the fact.
This, however, is not terribly helpful when it comes to saving lives. This is because aftershocks, by definition, are always less powerful than the initial earthquake. Usually, if a particular fault produces a sufficiently powerful earthquake, there will be a few aftershocks and then that'll be the end of the fireworks for a while. This isn't always the case, however. For example, the incredibly powerful earthquake that hit the New Madrid Fault on the Missouri-Tennessee border on December 16, 1811, evaluated by seismologists as magnitude 8.2, was followed just six hours later by another shock of about the same magnitude. And the fault was not yet quiesced: the December 16 quakes were succeeded by another magnitude 8.1 earthquake on January 23, and then yet another, even more powerful 8.3 earthquake on February 7. Which ones were the foreshocks? Which ones were the aftershocks? Any interpretation is about as useless as any other.
One of the more infamous cases involved a geophysicist named Brian Brady, who had a Ph.D. from MIT and worked at Colorado School of Mines. Brady asserted that a magnitude 9.2 earthquake-one of the largest in recorded history-would hit Lima, Peru, in 1981.40 His prediction initially had a fair amount of support in the seismological community-an early version of it had been coauthored with a USGS scientist. But as the theory became more elaborate-Brady would eventually invoke everything from the rock bursts he had observed in his studies of mines to Einstein's theory of relativity in support of it-colleagues had started telling him that theory was beyond their understanding:41 a polite way of saying that he was nuts. Eventually, he predicted that the magnitude 9.2 earthquake would be just one in a spectacular series in Peru, culminating in a magnitude 9.9 earthquake, the largest in recorded history, in August 1981.42
The prediction was leaked to the Peruvian media and terrified the population; this serious-seeming American scientist was sure their capital city would be in ruins. Their fear only intensified when it was reported that the Peruvian Red Cross had requested 100,000 body bags to prepare for the disaster. Tourism and property values declined,43 and the U.S. government eventually dispatched a team of scientists and diplomats to Peru in an effort to calm nerves. It made front-page news when there was no Great Peruvian Earthquake in 1981 (or even a minor one).
In figure 5-7a, I've plotted the historical frequencies of earthquakes near the 2011 epicenter in Japan.63 The data includes everything up through but not including the magnitude 9.1 earthquake on March 11. You'll see that the relationship almost follows the straight-line pattern that Gutenberg and Richter's method predicts. However, at about magnitude 7.5, there is a kink in the graph. There had been no earthquakes as large as a magnitude 8.0 in the region since 1964, and so the curve seems to bend down accordingly.
So how to connect the dots? If you go strictly by the Gutenberg-Richter law, ignoring the kink in the graph, you should still follow the straight line, as in figure 5-7b. Alternatively, you could go by what seismologists call a characteristic fit (figure 5-7c), which just means that it is descriptive of the historical frequencies of the earthquake in that area. In this case, that would mean that you took the kink in the historical data to be real-meaning, you thought there was some good reason why earthquakes larger than about magnitude 7.6 were unlikely to occur in the region.
Here is another example where an innocuous-seeming choice of assumptions will yield radically distinct conclusions-in this case, about the probability of a magnitude 9 earthquake in this part of Japan. The characteristic fit suggests that such an earthquake was nearly impossible-it implies that one might occur about every 13,000 years. The Gutenberg-Richter estimate, on the other hand, was that you'd get one such earthquake every three hundred years. That's infrequent but hardly impossible-a tangible enough risk that a wealthy nation like Japan might be able to prepare for it.64
The characteristic fit matched the recent historical record from a bit more snugly. But as we've learned, this type of pattern-matching is not always a good thing-it could imply an overfit model, in which case it will do a worse job of matching the true relationship. In this case, an overfit model would dramatically underestimate the likelihood of a catastrophic earthquake in the area. The problem with the characteristic fit is that it relied on an incredibly weak signal. As I mentioned, there had been no earthquake of magnitude 8 or higher in this region in the forty-five years or so prior to Tohoku. However, these are rare events to begin with: the Gutenberg-Richter law posits that they might occur only about once per thirty years in this area. It's not very hard at all for a once-per-thirty-year event to fail to occur in a forty-five-year window,65 no more so than a .300 hitter having a bad day at the plate and going 0-for-5.66 Meanwhile, there were quite a few earthquakes with magnitudes in the mid- to high 7's in this part of Japan. When such earthquakes had occurred in other parts of the world, they had almost always suggested the potential for larger ones. What justification was there to think that Japan would be a special case?
Actually, seismologists in Japan and elsewhere came up with a few rationalizations for that. They suggested, for instance, that the particular composition of the seafloor in the region, which is old and relatively cool and dense, might prohibit the formation of such large earthquakes.67 Some seismologists observed that, before 2004, no magnitude 9 earthquake had occurred in a region with that type of seafloor.
This was about like concluding that it was impossible for anyone from Pennsylvania to win the Powerball jackpot because no one had done so in the past three weeks. Magnitude 9 earthquakes, like lottery winners, are few and far between. Before 2004, in fact, only three of them had occurred in recorded history anywhere in the world. This wasn't nearly enough data to support such highly specific conclusions about the exact circumstances under which they might occur. Nor was Japan the first failure of such a theory; a similar one had been advanced about Sumatra68 at a time when it had experienced lots of magnitude 7 earthquakes69 but nothing stronger. Then the Great Sumatra Earthquake, magnitude 9.2,70 hit in December 2004.
The Gutenberg-Richter law would not have predicted the exact timing of the Sumatra or Japan earthquakes, but it would have allowed for their possibility.71 So far, it has held up remarkably well when a great many more elaborate attempts at earthquake prediction have failed.
Because they occur so rarely, it will take centuries to know what the true rate of magnitude 9 earthquakes is. It will take even longer to know whether earthquakes larger than magnitude 9.5 are possible. Hough told me that there may be some fundamental constraints on earthquake size from the geography of fault systems. If the largest continuous string of faults in the world ruptured together-everything from Tierra Del Fuego at the southern tip of South America all the way up through the Aleutians in Alaska-a magnitude 10 is about what you'd get, she said. But it is hard to know for sure.
# ch5
Earthquakes kill more people than hurricanes, in fact,16 despite seeming like the rarer phenomenon.17 Perhaps that is because they are so seldom predicted successfully. Whereas the landfall position of hurricanes can be forecasted at least three times more accurately now than they were even twenty-five years ago, the science of earthquake forecasting seems barely to have evolved since the ninth century A.D., when the Japanese first claimed to be able to anticipate earthquakes by looking at the behavior of catfish.18 (Cows, pigs, eels, rats, parakeets, seagulls, turtles, goldfish, and snakes have also been reported at various times to behave unusually in advance of an earthquake.)
We all know that California is very seismically active; the USGS estimates that an earthquake of magnitude 6.8 or higher will hit San Francisco about once every thirty-five years. Many of you will also know that Alaska has many earthquakes-the second largest one in recorded history, magnitude 9.4, hit Anchorage in 1964.
But did you know about Charleston, South Carolina? It is seismically active too; indeed, it experienced a magnitude 7.3 earthquake in 1886. The USGS estimates that there will be another big earthquake there about once per six hundred years. If you live in Seattle, you should probably have an earthquake plan ready; it is more earthquake-prone than many parts of California, the USGS says. But you don't need one if you live in Denver, which is a safe distance away from any continental boundaries.
If you compare the frequencies of earthquakes with their magnitudes, you'll find that the number drops off exponentially as the magnitude increases. While there are very few catastrophic earthquakes, there are literally millions of smaller ones-about 1.3 million earthquakes measuring between magnitude 2.0 and magnitude 2.9 around the world every year.27 Most of these earthquakes go undetected-certainly by human beings and often by seismometers.28 However, almost all earthquakes of magnitude 4.5 or greater are recorded today, however remote their location. Figure 5-3a shows the exponential decline in their frequencies, based on actual records of earthquakes from January 196429 through March 2012.30
According to the power law that Gutenberg and Richter uncovered, that means that an earthquake measuring between 6.0 and 6.9 should occur about once every thirty years in Tehran.
Furthermore, it follows that an earthquake that measured 7.0 or greater would occur about once every three hundred years near Tehran. This is the earthquake that Susan Hough fears. The Haiti earthquake of 2010, which measured magnitude 7.0 and killed 316,000,32 showed the apocalyptic consequences that earthquakes can produce in the developing world. Iran shares many of Haiti's problems-poverty, lax building codes, political corruption33-but it is much more densely populated. The USGS estimates, on the basis of high death tolls from smaller earthquakes in Iran, that between 15 and 30 percent of Tehran's population could die in the event of a catastrophic tremor there.34 Since there are about thirteen million people in Tehran's metro area, that would mean between two and four million fatalities.
Large earthquakes are almost always followed by dozens or even thousands of aftershocks (the 2011 earthquake in Japan produced at least 1,200 of them). These aftershocks follow a somewhat predictable pattern.35 Aftershocks are more likely to occur immediately after an earthquake than days later, and more likely to occur days later than weeks after the fact.
This, however, is not terribly helpful when it comes to saving lives. This is because aftershocks, by definition, are always less powerful than the initial earthquake. Usually, if a particular fault produces a sufficiently powerful earthquake, there will be a few aftershocks and then that'll be the end of the fireworks for a while. This isn't always the case, however. For example, the incredibly powerful earthquake that hit the New Madrid Fault on the Missouri-Tennessee border on December 16, 1811, evaluated by seismologists as magnitude 8.2, was followed just six hours later by another shock of about the same magnitude. And the fault was not yet quiesced: the December 16 quakes were succeeded by another magnitude 8.1 earthquake on January 23, and then yet another, even more powerful 8.3 earthquake on February 7. Which ones were the foreshocks? Which ones were the aftershocks? Any interpretation is about as useless as any other.
One of the more infamous cases involved a geophysicist named Brian Brady, who had a Ph.D. from MIT and worked at Colorado School of Mines. Brady asserted that a magnitude 9.2 earthquake-one of the largest in recorded history-would hit Lima, Peru, in 1981.40 His prediction initially had a fair amount of support in the seismological community-an early version of it had been coauthored with a USGS scientist. But as the theory became more elaborate-Brady would eventually invoke everything from the rock bursts he had observed in his studies of mines to Einstein's theory of relativity in support of it-colleagues had started telling him that theory was beyond their understanding:41 a polite way of saying that he was nuts. Eventually, he predicted that the magnitude 9.2 earthquake would be just one in a spectacular series in Peru, culminating in a magnitude 9.9 earthquake, the largest in recorded history, in August 1981.42
The prediction was leaked to the Peruvian media and terrified the population; this serious-seeming American scientist was sure their capital city would be in ruins. Their fear only intensified when it was reported that the Peruvian Red Cross had requested 100,000 body bags to prepare for the disaster. Tourism and property values declined,43 and the U.S. government eventually dispatched a team of scientists and diplomats to Peru in an effort to calm nerves. It made front-page news when there was no Great Peruvian Earthquake in 1981 (or even a minor one).
In figure 5-7a, I've plotted the historical frequencies of earthquakes near the 2011 epicenter in Japan.63 The data includes everything up through but not including the magnitude 9.1 earthquake on March 11. You'll see that the relationship almost follows the straight-line pattern that Gutenberg and Richter's method predicts. However, at about magnitude 7.5, there is a kink in the graph. There had been no earthquakes as large as a magnitude 8.0 in the region since 1964, and so the curve seems to bend down accordingly.
So how to connect the dots? If you go strictly by the Gutenberg-Richter law, ignoring the kink in the graph, you should still follow the straight line, as in figure 5-7b. Alternatively, you could go by what seismologists call a characteristic fit (figure 5-7c), which just means that it is descriptive of the historical frequencies of the earthquake in that area. In this case, that would mean that you took the kink in the historical data to be real-meaning, you thought there was some good reason why earthquakes larger than about magnitude 7.6 were unlikely to occur in the region.
Here is another example where an innocuous-seeming choice of assumptions will yield radically distinct conclusions-in this case, about the probability of a magnitude 9 earthquake in this part of Japan. The characteristic fit suggests that such an earthquake was nearly impossible-it implies that one might occur about every 13,000 years. The Gutenberg-Richter estimate, on the other hand, was that you'd get one such earthquake every three hundred years. That's infrequent but hardly impossible-a tangible enough risk that a wealthy nation like Japan might be able to prepare for it.64
The characteristic fit matched the recent historical record from a bit more snugly. But as we've learned, this type of pattern-matching is not always a good thing-it could imply an overfit model, in which case it will do a worse job of matching the true relationship. In this case, an overfit model would dramatically underestimate the likelihood of a catastrophic earthquake in the area. The problem with the characteristic fit is that it relied on an incredibly weak signal. As I mentioned, there had been no earthquake of magnitude 8 or higher in this region in the forty-five years or so prior to Tohoku. However, these are rare events to begin with: the Gutenberg-Richter law posits that they might occur only about once per thirty years in this area. It's not very hard at all for a once-per-thirty-year event to fail to occur in a forty-five-year window,65 no more so than a .300 hitter having a bad day at the plate and going 0-for-5.66 Meanwhile, there were quite a few earthquakes with magnitudes in the mid- to high 7's in this part of Japan. When such earthquakes had occurred in other parts of the world, they had almost always suggested the potential for larger ones. What justification was there to think that Japan would be a special case?
Actually, seismologists in Japan and elsewhere came up with a few rationalizations for that. They suggested, for instance, that the particular composition of the seafloor in the region, which is old and relatively cool and dense, might prohibit the formation of such large earthquakes.67 Some seismologists observed that, before 2004, no magnitude 9 earthquake had occurred in a region with that type of seafloor.
This was about like concluding that it was impossible for anyone from Pennsylvania to win the Powerball jackpot because no one had done so in the past three weeks. Magnitude 9 earthquakes, like lottery winners, are few and far between. Before 2004, in fact, only three of them had occurred in recorded history anywhere in the world. This wasn't nearly enough data to support such highly specific conclusions about the exact circumstances under which they might occur. Nor was Japan the first failure of such a theory; a similar one had been advanced about Sumatra68 at a time when it had experienced lots of magnitude 7 earthquakes69 but nothing stronger. Then the Great Sumatra Earthquake, magnitude 9.2,70 hit in December 2004.
The Gutenberg-Richter law would not have predicted the exact timing of the Sumatra or Japan earthquakes, but it would have allowed for their possibility.71 So far, it has held up remarkably well when a great many more elaborate attempts at earthquake prediction have failed.
Because they occur so rarely, it will take centuries to know what the true rate of magnitude 9 earthquakes is. It will take even longer to know whether earthquakes larger than magnitude 9.5 are possible. Hough told me that there may be some fundamental constraints on earthquake size from the geography of fault systems. If the largest continuous string of faults in the world ruptured together-everything from Tierra Del Fuego at the southern tip of South America all the way up through the Aleutians in Alaska-a magnitude 10 is about what you'd get, she said. But it is hard to know for sure.